The children were pronounced dead at the scene.
A tornado hit the small Central Texas city of Franklin, overturning mobile homes and damaging other residences, said Robertson County Sheriff Gerald Yezak.
Emergency Management Coordinator Billy Huggins said more than a dozen people were injured in Franklin, about 100 miles (160 kilometers) northeast of Austin.
The weather service said preliminary information showed an EF-3 tornado touched down with winds of 140 miles per hour.
The tornado destroyed 55 homes, a church, four businesses, a duplex, and part of the local housing authority building, authorities said. None of the injuries were thought to be life-threatening.
As the storms tore through MS overnight into Sunday, they left a trail of destruction that authorities are still combing through.
"It looks like a storm came up through Louisiana and into MS and exploded in Monroe County", Monroe County Sheriff Cecil Cantrell said. Another 19 were taken to hospitals, including two who were in critical condition. Alto is situated about 140 miles (225 kilometers) north of Houston. "We are just a mess".
The National Weather Service announced Sunday morning the Tornado Watch, saying a couple of tornadoes and isolated hail up to a quarter size possible. No injuries have been reported, but officials said several businesses and vehicles were damaged.
The roof of a hotel in New Albany, Mississippi, was damaged, although the cause was unclear. University spokesman Sid Salter said some debris, possibly carried by the tornado, was found on campus, but no injuries were reported and no buildings were damaged. Trees were down and at least some minor damage was reported in residential areas east of the campus.
Some of the storms could produce gusty winds and heavy rain with areas of fog after 9 p.m. Sunday, forecasters say.
Meantime a 13-year-old boy drowned in a drainage area in West Monroe, Louisiana, late Saturday afternoon, according to the Ouachita Parish Sheriff's Office. Damaging winds are expected to be the primary threat, but a few tornadoes are also possible. This system will bring with it a threat of severe weather both in the morning and again later afternoon on Sunday.